The following meanings apply in what follows:
“Meridian plane” is a plane containing the axis of rotation of the tire.                “Equatorial plane” is the plane passing through the middle of the tread surface of the tire and perpendicular to the axis of rotation of the tire.        “Radial direction” is a direction perpendicular to the axis of rotation of the tire.        “Axial direction” is a direction parallel to the axis of rotation of the tire.        “Circumferential direction” is a direction perpendicular to a meridian plane.        “Radial distance” is a distance measured at right angles to the axis of rotation of the tire and from the axis of rotation of the tire.        “Axial distance” is a distance measured parallel to the axis of rotation of the tire and from the equatorial plane.        “Radially” means in a radial direction.        “Axially” means in an axial direction.        “Radially on the inside of or radially on the outside of” means at a shorter, or longer, radial distance.        “Axially on the inside of or axially on the outside of” means at a shorter, or longer, axial distance.        
A tire comprises two beads that provide the mechanical connection between the tire and the rim on which it is mounted, the beads being respectively joined, by two sidewalls to a tread intended to come into contact with the ground via a tread surface.
A radial tire more specifically comprises a reinforcement comprising a crown reinforcement, radially on the inside of the tread, and a carcass reinforcement, radially on the inside of the crown reinforcement.
The carcass reinforcement of a radial tire for a heavy vehicle of the civil engineering type usually comprises at least one carcass reinforcement layer made up of metal reinforcing elements coated with a coating polymer material. The metal reinforcing elements are substantially parallel to one another and make an angle of between 85° and 95° with the circumferential direction. The carcass reinforcement layer comprises a main portion, that joins the two beads together and is wound, in each bead, around a bead wire core. The bead wire core comprises a circumferential reinforcing element usually made of metal, surrounded by at least one material which, nonexhaustively, may be made of polymer or textile. The winding of the carcass reinforcement layer around the bead wire core goes from the inside towards the outside of the tire to form a turned-back portion of carcass reinforcement, comprising an end. The turned-back portion of carcass reinforcement, in each bead, anchors the carcass reinforcement layer to the bead wire core of that bead.
Each bead comprises a filler element extending the bead wire core radially outwards. The filler element, in any meridian plane, has a substantially triangular cross section and is made of at least one filler polymer material. The filler element is generally made of a radial stack of at least two filler polymer materials in contact along a contact surface that intersects any meridian plane along a meridian line. The filler element axially separates the main portion of carcass reinforcement from the turned-back portion of carcass reinforcement.
A polymer material, after curing, is mechanically characterized by tensile stress-deformation characteristics that are determined by tensile testing. This tensile testing is performed by the person skilled in the art on a test specimen, in accordance with a known method, for example in accordance with international standard ISO 37, and under normal temperature (23±2° C.) and moisture (50±5% relative humidity) conditions defined by international standard ISO 471. The tensile stress measured for a 10% elongation of the test specimen is known as the elastic modulus at 10% elongation of a polymer blend and is expressed in mega pascals (MPa).
A polymer material, after curing, is also mechanically characterized by its hardness. Hardness is notably defined by the Shore A hardness determined in accordance with ASTM D 2240-86.
As the vehicle drives along, the tire, mounted on its rim, inflated and compressed under the load of the vehicle, is subjected to bending cycles, particularly at its beads and its sidewalls.
The bending cycles in particular lead to stresses and deformations primarily in shear and in compression in the filler polymer materials, because of the bending of the bead on the rim flange.
In particular, at the surface of contact between two filler polymer materials, the bending cycles initiate cracks which spread through the filler polymer material which is radially outermost and, over time, are likely to lead to degradation of the tire requiring it to be replaced.
According to the inventors, the initiation of cracks results from the gradient in rigidity between the radially innermost filler polymer material in contact with the bead wire core and the filler polymer material that is radially on the outside of it and adjacent along a contact surface. Deficiencies in cohesion between the two filler polymer materials along their contact surface is a factor that initiates cracking.
The rate at which the cracks spread is dependent firstly on the amplitude and frequency of the stress and strain deformation cycles and secondly on the respective rigidities of the filler polymer materials. By way of example, the elastic modulus at 10% elongation of the filler polymer material which is radially innermost and in contact with the bead wire core can be equal to 3 times the elastic modulus at 10% elongation of the filler polymer material which is radially on the outside of and adjacent to it.